A Short-support Dual Mask to the Piecewise Linears on a Uniform Triangulation

Approximation Theory X: Wavelets, Splines, and Applications
(2002)

Bruce Kessler, Western Kentucky University

Abstract

Much work has been done in finding duals and wavelets for a single scaling function on a triangulation (see [2], [4], [6] among others). The CBC algorithm allows the construction of duals with arbitrary approximation order at the expense of a larger support. This is an independent approach to the construction of a dual mask to the piecewise linear "hat" function on a uniform triangulation with a focus on maintaining the same hexagonal support. The associated wavelet masks are also constructed with only slightly larger supports.